Morphometrics is the technology of measuring biological shape and shape change. Over the last decade, its two main traditions, the algebraic and the geometric, have merged in a synthesis that combines the full power of multivariate analysis with contemporary computer visualization tools for the detection and interpretation of patterns involving landmark points, locations that are arguably homologous on biological grounds across the forms of a data set. The present grant has been specifically responsible for many components of that synthesis; the thin-plate spline interpolant between landmark configurations, the basis of partial warps that its bending-energy matrix generates for linearized descriptions of shape variation, many algebraic and diagrammatic approaches to within-sample and between sample landmark patterns, and preliminary extensions of all these to the analysis of outlines and of whole medical images. In the 1990's these techniques have showed their value wherever the morphometrics of landmarks has been applied, from craniofacial surgery through neuroanatomical atlas design to evolutionary biology. Over the period of this competing continuation we will focus on combining the new morphometric techniques with existing tools of image analysis in diverse applications across a range of typical biomedical concerns. Aim 1 involves extending the algebraic formalisms developed earlier for landmarks to include alternate bases for shape space, other spline formulas, and other registration systems for detecting informative dimensions of image variability. Aim 2 extends recent breakthroughs in the fusion of outline or surface information with landmark information, including the representation of edge directions in-between landmarks and their incorporation into shape predictions. Aim 3 explores novel and very promising versions of the important "image registration problem": combination of landmark features with image features, "horizontal" with "vertical," to improve the accuracy of diagnoses and prognoses. The algebraic and geometric methods developed here may permit extension of many of these strategies toward the next frontier of morphometric data, processes of normal or diseased development in which landmark-based descriptions become more complex over time. All these Aims overlap with a fourth, a continual emphasis upon visualization, simplification, exemplification, and dissemination to the growing community of consumers of this new morphometrics. Demonstration data sets will be drawn from cranio- facial surgery, cardiology, and neuroanatomy. The new techniques are intended to become crucial software tools for routine scientific exploitation of clinical medical images. Diverse image-based empirical studies will thereby continue to gain both in statistical efficiency and int eh effectiveness with which information is extracted for clinical and comparative purposes.